Find value of K such that there is no unique solutions for the following system of equations.

3x + y - z = 1 (1)

x -y +kz =7 (2)

2x+ky-z=-1 (3)

DO not use that method/set up bellow. I want to solve simultaneously manipulating eqns...

3...1..-1

1..-1...k

2...k..-1

Must use simultaneous to solve for K... so far I got

(2)x3 -(1).............. -4y+3kz+z =20 (4)

(2)x2 - (3) -2y-ky+2kz-z=15 (5)

(5)x2 - (4) -2ky+kz-3z=10

now what? Hope My steps so far are right...

(note answer is K=1 K=-2/3)

Note: I cannot use this method:

|3 1 -1|3 1|

|1 -1 k|1 -1| =

|2 k -1|2 k|

Cheers.

I've tried my best so far but I just can't seem to get it. Thanks